find the derivative of the following functions:
1. invsin(x)
2.invcos(x)
3. invtan(x)
4. invcsc(x)
5. invsec(x)
6. invcot(x)
What is
1. 1/(1-(x^2))^.5
2. -1/(1-(x^2))^.5
3. 1/((x^2)+1)
4. -1/(|x|((x^2)-1)^.5)
5. 1/(|x|((x^2)-1)^.5)
6. -1/((x^2)+1)
100
Water is taken from a conical reservoir 20 ft. in diameter and 50 ft. deep at a constant rate of 12ft^3/min. How fast is the water level changing when the depth of the water is 20ft?
Do step 1. (draw a picture)
What is on board
100
Find the linearization of f(x) = (x^3) + 3(x^2) at a = 1
What is
L(x)=9x-5
200
find dy/dx if cos(xy)=sinx-sec10y
What is (cosx+ysin(xy))/(-xsin(xy)+10sec(10y)tan(10y))
200
find the derivative of y=ln(lnx)
What is 1/xlnx
200
find dy/dx if y=(x^2)invcosx
What is
(x^2)(-1/(1-(x^2))^.5 + (invcosx)(2x)
200
Do step 2 (identify knowns, unknowns, and what you want to solve)
What is
Givens:
dv/dt = -12 ft^3/min
h = 20 ft
Unknowns:
V, r, dr/dt, dh/dt
Trying to solve for:
dh/dt
200
Find the linearization of f(x) = x/(x+2)^2
What is
L(x) = (1/9) + (1/27)(x-1)
300
find dy/dx if x^(2/3) + y^(2/3) = 8
What is -y^(1/3)/x^(1/3)
300
Find the derivative of y= ln(6/(x^2)((x+7)^3))
What is -(2/x) - (3/(x+7))
300
find dy/dx if y = (1+invtanx)/(2-3invtanx)
What is
5/(1+(x^2))(2-3invtanx)^2
300
Do step 3 (write equation relating the vbls you know and want to solve for)
What is
V = (1/3)(pi)(r^2)(h)
10/50 = r/h, so r = .2h
SO:
V = (pi/75)(h^3)
300
find dy if 4(x^2) + 7xy + 5 = 0
What is
dy= (-7y-8x)dx/7x
400
Find the eq. of the tangent line and normal line to the curve (x^2) + 2xy - (y^2) + x = 2 at the point (0,1)
What is Tangent line: y = (3/2)x+1
norm line: (-2/3)x+1
400
Use logarithmic differentiation to find dy/dx if
y= ((2 * (x^3) + x -2)^(1/3))/((x^3) * cosx)
What is ((6(x^2)+1)/(6(x^3)+3x-6) -(3/x) +tanx)*((2(x^3)+x-2)^(1/3)/(x^3)(cosx))
400
find dy/dx if y=2x+7invcotx
What is
2-(7/((x^2)+1)
400
Do step 4 (take derivative with respect to t)
What is
dV/dt = (pi/25)(h^2)(dh/dt)
400
find dy if y=(x^2) + sinx
What is
dy = (2x + cosx)dx
500
Find the 1st and 2nd derive as functions of only x and y if
(x^3) + (y^3) = 10